Almkvist-Giullera formula for pi: Difference between revisions

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<syntaxhighlight lang=11l>F isqrt(BigInt =x)

<syntaxhighlight lang="11l">F isqrt(BigInt =x)

BigInt q = 1

BigInt r = 0

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=={{header|AArch64 Assembly}}==

{{works with|as|Raspberry Pi 3B version Buster 64 bits or android 64 bits with application Termux }}

/* ARM assembly AARCH64 Raspberry PI 3B */

/* program calculPi64.s */

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=={{header|ARM Assembly}}==

{{works with|as|Raspberry Pi or android 32 bits with application Termux}}

/* ARM assembly Raspberry PI */

/* program calculPi.s */

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A little challenging due to lack of BigFloat or BigRational. Note the extended precision integers displayed for each term, not extended precision floats. Also features the next term based on the last term, rather than computing each term from scratch. And the multiply by 32, divide by 3 is reserved for final sum, instead of each term (except for the 0..9th displayed terms).

<syntaxhighlight lang=csharp>using System;

<syntaxhighlight lang="csharp">using System;

using BI = System.Numerics.BigInteger;

using static System.Console;

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<syntaxhighlight lang=cpp>#include <boost/multiprecision/cpp_dec_float.hpp>

<syntaxhighlight lang="cpp">#include <boost/multiprecision/cpp_dec_float.hpp>

#include <boost/multiprecision/gmp.hpp>

#include <iomanip>

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<syntaxhighlight lang=lisp>(ql:quickload :computable-reals :silent t)

<syntaxhighlight lang="lisp">(ql:quickload :computable-reals :silent t)

(use-package :computable-reals)

(setq *print-prec* 70)

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=={{header|dc}}==

<syntaxhighlight lang=dc>[* factorial *]sz

<syntaxhighlight lang="dc">[* factorial *]sz

[ 1 Sp [ d lp * sp 1 - d 1 <f ]Sf d 1 <f Lfsz sz Lp ]sF

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However, Erlang does not have much in the way of calculating with large integers beyond basic arithmetic, so this version implements integer powers, logs, square roots, as well as the factorial function.

-mode(compile).

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=={{header|F_Sharp|F#}}==

This task uses [[Isqrt_(integer_square_root)_of_X#F.23]]

// Almkvist-Giullera formula for pi. Nigel Galloway: August 17th., 2021

let factorial(n:bigint)=MathNet.Numerics.SpecialFunctions.Factorial n

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=={{header|Factor}}==

<syntaxhighlight lang=factor>USING: continuations formatting io kernel locals math

<syntaxhighlight lang="factor">USING: continuations formatting io kernel locals math

math.factorials math.functions sequences ;

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=={{header|Go}}==

<syntaxhighlight lang=go>package main

<syntaxhighlight lang="go">package main

import (

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<syntaxhighlight lang=haskell>import Control.Monad

<syntaxhighlight lang="haskell">import Control.Monad

import Data.Number.CReal

import GHC.Integer

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sqrt is noticeably slow, bringing execution time to over 1 second. I'm not sure if it's because it's coded imperatively using traditional loops vs. J point-free style, or if it's due to the fact that the numbers are very large. I suspect the latter since it only takes 4 iterations of Heron's method to get the square root.

numerator =: monad define "0

(3 * (! x: y)^6) %~ 32 * (!6x*y) * (y*(126 + 532*y)) + 9x

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{{libheader|es-main}} to support use of module as main code

<syntaxhighlight lang=javascript>import esMain from 'es-main';

<syntaxhighlight lang="javascript">import esMain from 'es-main';

import { BigFloat, set_precision as SetPrecision } from 'bigfloat-esnext';

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'''Preliminaries'''

<syntaxhighlight lang=jq># A reminder to include the "rational" module:

<syntaxhighlight lang="jq"># A reminder to include the "rational" module:

# include "rational";

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end; </syntaxhighlight>

'''Almkvist-Giullera Formula'''

def almkvistGiullera(print):

. as $n

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end; </syntaxhighlight>

'''The Tasks'''

def task1:

"N Integer Portion Pow Nth Term",

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=={{header|Julia}}==

<syntaxhighlight lang=julia>using Formatting

<syntaxhighlight lang="julia">using Formatting

setprecision(BigFloat, 300)

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=={{header|Mathematica}}/{{header|Wolfram Language}}==

<syntaxhighlight lang=~~Mathematica~~>ClearAll[numerator, denominator]

<syntaxhighlight lang="mathematica">ClearAll[numerator, denominator]

numerator[n_] := (2^5) ((6 n)!) (532 n^2 + 126 n + 9)/(3 (n!)^6)

denominator[n_] := 10^(6 n + 3)

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Derived from Wren version with some simplifications.

<syntaxhighlight lang=~~Nim~~>import strformat, strutils

<syntaxhighlight lang="nim">import strformat, strutils

import decimal

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=={{header|Perl}}==

<syntaxhighlight lang=perl>use strict;

<syntaxhighlight lang="perl">use strict;

use warnings;

use feature qw(say);

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=={{header|Phix}}==

with javascript_semantics

requires("1.0.0")

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=={{header|PicoLisp}}==

<syntaxhighlight lang=~~PicoLisp~~>(scl 70)

<syntaxhighlight lang="picolisp">(scl 70)

(de fact (N)

(if (=0 N)

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=={{header|Python}}==

<syntaxhighlight lang=python>import mpmath as mp

<syntaxhighlight lang="python">import mpmath as mp

with mp.workdps(72):

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=={{header|Quackery}}==

<syntaxhighlight lang=~~Quackery~~> [ $ "bigrat.qky" loadfile ] now!

<syntaxhighlight lang="quackery"> [ $ "bigrat.qky" loadfile ] now!

[ 1 swap times [ i^ 1+ * ] ] is ! ( n --> n )

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=={{header|Raku}}==

<syntaxhighlight lang=~~perl6~~># 20201013 Raku programming solution

<syntaxhighlight lang="raku" line># 20201013 Raku programming solution

use BigRoot;

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=={{header|REXX}}==

<syntaxhighlight lang=rexx>/*REXX program uses the Almkvist─Giullera formula for 1 / (pi**2) [or pi ** -2]. */

<syntaxhighlight lang="rexx">/*REXX program uses the Almkvist─Giullera formula for 1 / (pi**2) [or pi ** -2]. */

numeric digits length( pi() ) + length(.); w= 102

say $( , 3) $( , w%2) $('power', 5) $( , w)

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=={{header|Sidef}}==

<syntaxhighlight lang=ruby>func almkvist_giullera(n) {

<syntaxhighlight lang="ruby">func almkvist_giullera(n) {

(32 * (14*n * (38*n + 9) + 9) * (6*n)!) / (3 * n!**6)

}

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<syntaxhighlight lang=vbnet>Imports System, BI = System.Numerics.BigInteger, System.Console

<syntaxhighlight lang="vbnet">Imports System, BI = System.Numerics.BigInteger, System.Console

Module Module1

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<syntaxhighlight lang=ecmascript>import "/big" for BigInt, BigRat

<syntaxhighlight lang="ecmascript">import "/big" for BigInt, BigRat

import "/fmt" for Fmt